Traditional barbed fluid connectors seal on the interior surface of a piece of flexible tubing. This presents various challenges or problems. For example, such a construction can present a location for trapping the fluid under the barb or barbs, and causing contamination of the fluid system. It can also be difficult inserting the end of the flexible tubing over the barbed end of a connector, especially with larger diameter tubing. Finally, the inner diameter of the barbed connector is typically smaller than the inner diameter of the flexible tubing. Therefore, the barbed connector can present an undesirable restriction in fluid flow.